Rational Numbers on the Number Line

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SWBAT place positive and negative rational numbers in order using a number line.

Big Idea

The number line is a useful tool when ordering positive and negative rational numbers


10 minutes

SMP 2,5,6

I’m going to have the students working on a problem that will require them to use the number line to solve.  This problem is typical when dealing with integers and students usually struggle to find the solution or they get the solution wrong because they forget that they are looking at the whole difference above and below zero.

The problem is simply stated and it will be important to remind students that they have a tool to use to be able to solve this problem.  Allow students time to think about and come up with a strategy for solving.  

More Uses for the Number Line

15 minutes

SMP 5 and 6

The purpose of this lesson is to use the number line to show students how to order positive and negative rational numbers.  At no time should students be changing the fractions to decimals or percents and vice versa.

I’m going to bring students back to the number line showing positive and negative whole numbers.  I want students to remember that for every positive whole number, there is a negative whole number the same distance from zero.  If whole numbers have opposites then so do other rational numbers.  Go over rational number:  any number that can be written as a fraction including terminating and repeating decimals.  I will be showing them the benchmark fractions on the number line (1/2, ¼, ¾, and so on) and then showing them their opposites. 

We will also discuss strategies for placing fractions on the number line at this time.  Students should know to use benchmark fractions or make equal marks between the whole numbers.  

Placing Rational Numbers on the Number Line

45 minutes

SMP 1,2,3,5,6

I chose each of these problems because they were surrounded by real world context.  Making sense of this concept is difficult for students so to put within some context helps make sense and meaning of what is happening.

My plan is to do one problem with them and let them work independently on the next.  So every other problem will be independent work for them.  I’ve marked this in the power point.  If students are not grasping this or are really struggling, you can work each problem out as a group.  Students should draw a number line on their paper.  Make sure they use enough space between the whole numbers to make appropriate marks.  As you go through each problem, remind students to think about zero and where the numbers should be placed in relationship to it.  So, have them separate the positive and the negative numbers.  Work with the positive side first, students should be able to place these numbers easily.  Then work on the negative side. Students should use benchmark fractions or appropriate markings to locate these numbers.  Remind students that even though the rational number is negative, it’s still the same distance from zero as its opposite.

As students are working independently on their number lines, ask them how they know they are correct?  What made them decide to locate their rational number?

One of the independent work problems is from Illustrative mathematics.


15 minutes

Students will be completing a comprehension menu and turning this in for evidence of student learning and understanding.